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Stability of Inverse Pitchfork Domination | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 81، دوره 12، شماره 1، مرداد 2021، صفحه 1009-1016 اصل مقاله (318.42 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4956 | ||
| نویسنده | ||
| Mohammed A. Abdlhusein* | ||
| Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq | ||
| تاریخ دریافت: 10 مهر 1399، تاریخ بازنگری: 17 آذر 1399، تاریخ پذیرش: 30 دی 1399 | ||
| چکیده | ||
| There are few papers deals with stability of the inverse domination number in graphs by adding new edge to the graph or removing edge or vertex. Before this type of study, we need to know the stability of the domination number, then check the stability of the inverse domination. In this paper, the inverse pitchfork domination number $\gamma_{pf}^{-1}(G)$ is studied to be changing or not after adding or removing edge or removing vertex. Some conditions are putted on the graph to be affected or not with several results and examples. | ||
| کلیدواژه‌ها | ||
| dominating set؛ pitchfork domination؛ inverse pitchfork domination | ||
| مراجع | ||
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[1] M.A. Abdlhusein, Doubly connected bi-domination in graphs, Discrete Math. Algorithm Appl. 13(2) (2021) 2150009. [2] M.A. Abdlhusein, Applying the (1, 2)-pitchfork domination and its inverse on some special graphs, Bol. Soc. Paran. Mat. accepted to appear (2021). [3] M.A. Abdlhusein and M.N. Al-Harere, New parameter of inverse domination in graphs, Indian J. Pure Appl. Math. accepted to appear (2021). [4] M.A. Abdlhusein and M.N. Al-Harere, Some modified types of pitchfork domination and its inverse, Bol. Soc. Paran. Mat., accepted to appear (2021). [5] M. N. Al-Harere and M. A. Abdlhusein, Pitchfork domination in graphs, Discrete Math. Algorithm Appl. 12(2) (2020) 2050025. [6] M.N. Al-Harere and P.A. Khuda Bakhash, Changes of tadpole domination number upon changing of graphs, Sci. Int. 31(2) (2019) 197-199. [7] M.N. Al-harere and P.A. Khuda, Tadpole domination in duplicated graphs, Discrete Math. Algorithms Appl. 13(2) (2021) 2150003. [8] M. Amraee, N.J. Rad and M. Maghasedi, Roman domination stability in graphs, Math. Rep. 21(71) (2019) 193-204. [9] B.A. Atakul, Stability and domination exponentially in some graphs, AIMS Math. 5(5) (2020) 5063-5075. [10] K. Attalah and M. Chellali, 2-Domination dot-stable and dot-critical graphs, Asian-Eur. J. Math. 21(5) (2021) 2150010. [11] S. Balamurugan, Changing and unchanging isolate domination: edge removal, Discrete Math. Algorithms Appl. 9(1) (2017) 1750003. [12] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker Inc., New York, 1998. [13] M.A. Henning and M. Krzywkowski, Total domination stability in graphs, Discrete Appl. Math. 236(19) (2018) 246-255. [14] A.A. Omran and T.A. Ibrahim, Fuzzy co-even domination of strong fuzzy graphs, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 727-734. [15] S.J. Radhi, M.A. Abdlhusein and A.E. Hashoosh, The arrow domination in graphs, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 473-480. [16] M.S. Rahman, Basic Graph Theory, Springer, India, 2017. [17] V. Samodivkin, A note on Roman domination: changing and unchanging, Aust. J. Combin. 71(2) (2018) 303-311. | ||
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